TSTP Solution File: KLE011+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE011+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 02:28:00 EDT 2022
% Result : Theorem 5.29s 5.47s
% Output : Refutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of clauses : 63 ( 27 unt; 0 nHn; 63 RR)
% Number of literals : 113 ( 0 equ; 63 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
test__dfg(skc3),
file('KLE011+2.p',unknown),
[] ).
cnf(2,axiom,
test__dfg(skc2),
file('KLE011+2.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(u,u),u),
file('KLE011+2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,one),u),
file('KLE011+2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(one,u),u),
file('KLE011+2.p',unknown),
[] ).
cnf(11,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE011+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE011+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE011+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ complement(u,v)
| equal(multiplication(v,u),zero) ),
file('KLE011+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ complement(u,v)
| equal(multiplication(u,v),zero) ),
file('KLE011+2.p',unknown),
[] ).
cnf(17,axiom,
( ~ complement(u,v)
| equal(addition(v,u),one) ),
file('KLE011+2.p',unknown),
[] ).
cnf(18,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE011+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ test__dfg(u)
| ~ equal(c(u),v)
| complement(u,v) ),
file('KLE011+2.p',unknown),
[] ).
cnf(22,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE011+2.p',unknown),
[] ).
cnf(23,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE011+2.p',unknown),
[] ).
cnf(24,axiom,
( ~ equal(addition(u,v),one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
file('KLE011+2.p',unknown),
[] ).
cnf(25,axiom,
( ~ leq(one,addition(addition(multiplication(addition(skc2,c(skc2)),skc3),multiplication(addition(skc3,c(skc3)),skc2)),multiplication(c(skc3),c(skc2))))
| ~ leq(addition(addition(multiplication(addition(skc2,c(skc2)),skc3),multiplication(addition(skc3,c(skc3)),skc2)),multiplication(c(skc3),c(skc2))),one) ),
file('KLE011+2.p',unknown),
[] ).
cnf(26,plain,
( ~ leq(one,addition(multiplication(skc3,skc2),addition(multiplication(c(skc3),skc2),addition(multiplication(skc2,skc3),addition(multiplication(c(skc2),skc3),multiplication(c(skc3),c(skc2)))))))
| ~ leq(addition(multiplication(skc3,skc2),addition(multiplication(c(skc3),skc2),addition(multiplication(skc2,skc3),addition(multiplication(c(skc2),skc3),multiplication(c(skc3),c(skc2)))))),one) ),
inference(rew,[status(thm),theory(equality)],[18,25,11,23]),
[iquote('0:Rew:18.0,25.1,18.0,25.1,18.0,25.1,11.0,25.1,23.0,25.1,18.0,25.1,18.0,25.1,11.0,25.1,23.0,25.1,11.0,25.1,18.0,25.1,18.0,25.0,18.0,25.0,18.0,25.0,11.0,25.0,23.0,25.0,18.0,25.0,18.0,25.0,11.0,25.0,23.0,25.0,11.0,25.0,18.0,25.0')] ).
cnf(27,plain,
( ~ equal(c(skc2),u)
| complement(skc2,u) ),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.0')] ).
cnf(30,plain,
( ~ equal(c(skc3),u)
| complement(skc3,u) ),
inference(res,[status(thm),theory(equality)],[1,20]),
[iquote('0:Res:1.0,20.0')] ).
cnf(58,plain,
( ~ complement(u,v)
| equal(addition(u,v),one) ),
inference(spr,[status(thm),theory(equality)],[17,11]),
[iquote('0:SpR:17.1,11.0')] ).
cnf(80,plain,
complement(skc3,c(skc3)),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.0')] ).
cnf(93,plain,
complement(skc2,c(skc2)),
inference(eqr,[status(thm),theory(equality)],[27]),
[iquote('0:EqR:27.0')] ).
cnf(99,plain,
( ~ equal(u,u)
| leq(u,u) ),
inference(spl,[status(thm),theory(equality)],[4,14]),
[iquote('0:SpL:4.0,14.0')] ).
cnf(105,plain,
leq(u,u),
inference(obv,[status(thm),theory(equality)],[99]),
[iquote('0:Obv:99.0')] ).
cnf(185,plain,
equal(addition(u,addition(v,w)),addition(w,addition(u,v))),
inference(spr,[status(thm),theory(equality)],[18,11]),
[iquote('0:SpR:18.0,11.0')] ).
cnf(194,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[4,18]),
[iquote('0:SpR:4.0,18.0')] ).
cnf(197,plain,
equal(addition(addition(u,v),w),addition(v,addition(u,w))),
inference(spr,[status(thm),theory(equality)],[11,18]),
[iquote('0:SpR:11.0,18.0')] ).
cnf(206,plain,
equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
inference(rew,[status(thm),theory(equality)],[18,197]),
[iquote('0:Rew:18.0,197.0')] ).
cnf(207,plain,
( ~ leq(one,addition(multiplication(skc3,skc2),addition(multiplication(skc2,skc3),addition(multiplication(c(skc3),skc2),addition(multiplication(c(skc2),skc3),multiplication(c(skc3),c(skc2)))))))
| ~ leq(addition(multiplication(skc3,skc2),addition(multiplication(c(skc3),skc2),addition(multiplication(skc2,skc3),addition(multiplication(c(skc2),skc3),multiplication(c(skc3),c(skc2)))))),one) ),
inference(rew,[status(thm),theory(equality)],[206,26]),
[iquote('0:Rew:206.0,26.0')] ).
cnf(210,plain,
( ~ leq(one,addition(multiplication(skc2,skc3),addition(multiplication(skc3,skc2),addition(multiplication(c(skc2),skc3),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2)))))))
| ~ leq(addition(multiplication(skc2,skc3),addition(multiplication(skc3,skc2),addition(multiplication(c(skc2),skc3),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2)))))),one) ),
inference(rew,[status(thm),theory(equality)],[206,207]),
[iquote('0:Rew:206.0,207.1,206.0,207.1,206.0,207.1,206.0,207.0,206.0,207.0')] ).
cnf(222,plain,
( ~ complement(u,v)
| equal(addition(u,one),one) ),
inference(spr,[status(thm),theory(equality)],[58,194]),
[iquote('0:SpR:58.1,194.0')] ).
cnf(278,plain,
( ~ complement(u,v)
| equal(multiplication(one,w),addition(multiplication(v,w),multiplication(u,w))) ),
inference(spr,[status(thm),theory(equality)],[17,23]),
[iquote('0:SpR:17.1,23.0')] ).
cnf(290,plain,
( ~ complement(u,v)
| equal(addition(multiplication(v,w),multiplication(u,w)),w) ),
inference(rew,[status(thm),theory(equality)],[6,278]),
[iquote('0:Rew:6.0,278.1')] ).
cnf(308,plain,
( ~ complement(u,v)
| equal(multiplication(w,one),addition(multiplication(w,v),multiplication(w,u))) ),
inference(spr,[status(thm),theory(equality)],[17,22]),
[iquote('0:SpR:17.1,22.0')] ).
cnf(320,plain,
( ~ complement(u,v)
| equal(addition(multiplication(w,v),multiplication(w,u)),w) ),
inference(rew,[status(thm),theory(equality)],[5,308]),
[iquote('0:Rew:5.0,308.1')] ).
cnf(334,plain,
( ~ complement(u,v)
| ~ equal(one,one)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(spl,[status(thm),theory(equality)],[58,24]),
[iquote('0:SpL:58.1,24.0')] ).
cnf(348,plain,
( ~ complement(u,v)
| ~ equal(multiplication(v,u),zero)
| ~ equal(multiplication(u,v),zero)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[334]),
[iquote('0:Obv:334.1')] ).
cnf(349,plain,
( ~ complement(u,v)
| ~ equal(zero,zero)
| ~ equal(zero,zero)
| complement(v,u) ),
inference(rew,[status(thm),theory(equality)],[16,348,15]),
[iquote('0:Rew:16.1,348.2,15.1,348.1')] ).
cnf(350,plain,
( ~ complement(u,v)
| complement(v,u) ),
inference(obv,[status(thm),theory(equality)],[349]),
[iquote('0:Obv:349.2')] ).
cnf(589,plain,
complement(c(skc3),skc3),
inference(res,[status(thm),theory(equality)],[80,350]),
[iquote('0:Res:80.0,350.0')] ).
cnf(590,plain,
complement(c(skc2),skc2),
inference(res,[status(thm),theory(equality)],[93,350]),
[iquote('0:Res:93.0,350.0')] ).
cnf(812,plain,
equal(addition(u,addition(v,w)),addition(addition(u,w),v)),
inference(spr,[status(thm),theory(equality)],[206,11]),
[iquote('0:SpR:206.0,11.0')] ).
cnf(900,plain,
equal(addition(u,addition(v,w)),addition(u,addition(w,v))),
inference(rew,[status(thm),theory(equality)],[18,812]),
[iquote('0:Rew:18.0,812.0')] ).
cnf(2106,plain,
( ~ complement(u,v)
| equal(addition(multiplication(v,w),addition(x,multiplication(u,w))),addition(x,w)) ),
inference(spr,[status(thm),theory(equality)],[290,206]),
[iquote('0:SpR:290.1,206.0')] ).
cnf(2328,plain,
( ~ complement(u,v)
| equal(addition(multiplication(w,v),w),w) ),
inference(spr,[status(thm),theory(equality)],[320,194]),
[iquote('0:SpR:320.1,194.0')] ).
cnf(2377,plain,
( ~ complement(c(skc2),skc2)
| ~ leq(one,addition(multiplication(skc2,skc3),addition(multiplication(skc3,skc2),addition(multiplication(c(skc2),skc3),addition(multiplication(c(skc3),skc2),multiplication(c(skc3),c(skc2)))))))
| ~ leq(addition(multiplication(skc2,skc3),addition(multiplication(skc3,skc2),addition(multiplication(c(skc2),skc3),c(skc3)))),one) ),
inference(spl,[status(thm),theory(equality)],[320,210]),
[iquote('0:SpL:320.1,210.1')] ).
cnf(2378,plain,
( ~ complement(u,v)
| equal(addition(w,multiplication(w,v)),w) ),
inference(rew,[status(thm),theory(equality)],[11,2328]),
[iquote('0:Rew:11.0,2328.1')] ).
cnf(2412,plain,
( ~ complement(c(skc2),skc2)
| ~ leq(one,addition(c(skc3),addition(multiplication(skc2,skc3),addition(multiplication(skc3,skc2),multiplication(c(skc2),skc3)))))
| ~ leq(addition(c(skc3),addition(multiplication(skc2,skc3),addition(multiplication(skc3,skc2),multiplication(c(skc2),skc3)))),one) ),
inference(rew,[status(thm),theory(equality)],[206,2377,185,320]),
[iquote('0:Rew:206.0,2377.2,185.0,2377.2,206.0,2377.1,185.0,2377.1,320.1,2377.1')] ).
cnf(2413,plain,
( ~ complement(c(skc2),skc2)
| ~ leq(one,addition(c(skc3),skc3))
| ~ leq(addition(c(skc3),skc3),one) ),
inference(rew,[status(thm),theory(equality)],[2378,2412,900,2106]),
[iquote('0:Rew:2378.1,2412.2,900.0,2412.2,2106.1,2412.2,2378.1,2412.1,900.0,2412.1,2106.1,2412.1')] ).
cnf(2414,plain,
( ~ complement(c(skc2),skc2)
| ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(addition(skc3,c(skc3)),one) ),
inference(rew,[status(thm),theory(equality)],[11,2413]),
[iquote('0:Rew:11.0,2413.2,11.0,2413.1')] ).
cnf(2415,plain,
( ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(addition(skc3,c(skc3)),one) ),
inference(mrr,[status(thm)],[2414,590]),
[iquote('0:MRR:2414.0,590.0')] ).
cnf(2420,plain,
equal(addition(skc3,one),one),
inference(res,[status(thm),theory(equality)],[80,222]),
[iquote('0:Res:80.0,222.0')] ).
cnf(2429,plain,
equal(addition(c(skc3),one),one),
inference(res,[status(thm),theory(equality)],[589,222]),
[iquote('0:Res:589.0,222.0')] ).
cnf(2436,plain,
equal(addition(one,skc3),one),
inference(rew,[status(thm),theory(equality)],[11,2420]),
[iquote('0:Rew:11.0,2420.0')] ).
cnf(2438,plain,
equal(addition(one,c(skc3)),one),
inference(rew,[status(thm),theory(equality)],[11,2429]),
[iquote('0:Rew:11.0,2429.0')] ).
cnf(2455,plain,
equal(addition(one,addition(skc3,u)),addition(one,u)),
inference(spr,[status(thm),theory(equality)],[2436,18]),
[iquote('0:SpR:2436.0,18.0')] ).
cnf(16181,plain,
( ~ leq(one,addition(skc3,u))
| equal(addition(skc3,u),addition(one,u)) ),
inference(spr,[status(thm),theory(equality)],[2455,13]),
[iquote('0:SpR:2455.0,13.1')] ).
cnf(16396,plain,
( ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(addition(one,c(skc3)),one) ),
inference(rew,[status(thm),theory(equality)],[16181,2415]),
[iquote('0:Rew:16181.1,2415.1')] ).
cnf(16414,plain,
( ~ leq(one,addition(skc3,c(skc3)))
| ~ leq(one,one) ),
inference(rew,[status(thm),theory(equality)],[2438,16396]),
[iquote('0:Rew:2438.0,16396.1')] ).
cnf(16415,plain,
~ leq(one,addition(skc3,c(skc3))),
inference(mrr,[status(thm)],[16414,105]),
[iquote('0:MRR:16414.1,105.0')] ).
cnf(16556,plain,
( ~ complement(skc3,c(skc3))
| ~ leq(one,one) ),
inference(spl,[status(thm),theory(equality)],[58,16415]),
[iquote('0:SpL:58.1,16415.0')] ).
cnf(16563,plain,
$false,
inference(mrr,[status(thm)],[16556,80,105]),
[iquote('0:MRR:16556.0,16556.1,80.0,105.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE011+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 10:08:26 EDT 2022
% 0.14/0.35 % CPUTime :
% 5.29/5.47
% 5.29/5.47 SPASS V 3.9
% 5.29/5.47 SPASS beiseite: Proof found.
% 5.29/5.47 % SZS status Theorem
% 5.29/5.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.29/5.47 SPASS derived 10907 clauses, backtracked 0 clauses, performed 0 splits and kept 3013 clauses.
% 5.29/5.47 SPASS allocated 109458 KBytes.
% 5.29/5.47 SPASS spent 0:00:05.04 on the problem.
% 5.29/5.47 0:00:00.03 for the input.
% 5.29/5.47 0:00:00.03 for the FLOTTER CNF translation.
% 5.29/5.47 0:00:00.10 for inferences.
% 5.29/5.47 0:00:00.00 for the backtracking.
% 5.29/5.47 0:00:04.84 for the reduction.
% 5.29/5.47
% 5.29/5.47
% 5.29/5.47 Here is a proof with depth 5, length 63 :
% 5.29/5.47 % SZS output start Refutation
% See solution above
% 5.29/5.47 Formulae used in the proof : goals additive_idempotence multiplicative_right_identity multiplicative_left_identity additive_commutativity order test_2 additive_associativity test_3 right_distributivity left_distributivity
% 5.29/5.47
%------------------------------------------------------------------------------